With ANY option besides Walk-Lotus, the Gifts player has to pass the turn,
Anusien, I think Brassman is right. The problem here is that if he has Yawg and we give him Lotus then he can go Lotus, Yawg, Lotus, Tinker and pass the turn with DSC in play and crucially no artifact in the yard.
Even worse, my split gives him Walk in hand so he can win next turn. If you instead give him Academy then he does not win next turn but he does have a lot of mana although getting 4 is not that important given the list he is playing and the fact that he already cast Gifts. I can see that Academy, Lotus is better than Lotus, Walk with Yawg in hand, but both have the fatal flaw that they allow him to Tinker for DSC with no artifact in the yard now.
This leaves Echoing Truth as basically our only out.
All this only matters if he has Yawg in hand. I do not think that a Tutor for Yawg really does enough unless he is holding more acceleration which is unfortunately entirely possible.
If he really has Yawg in hand, then I am not sure I understand having Academy in that pile.
With Vamp or Demonic in hand Academy still does not make much sense to me since he would need BB in order to tutor up and cast Yawg and he will not have that unless he is holding Petal or uses his land drop to find B. Why Academy?
Academy makes most sense in conjunction with Mystical Tutor. Academy allows him to use Island to Mystical for Yawg on upkeep. Then Academy + Jet are all that is needed to Cast Yawg on the next turn.
Although I agree with AngryPheldagrif and Brassman that this pile implies access to Yawg I think that Academy implies that the access to Yawg is provided by Mystical Tutor.
Which split makes the most sense if your opponent is holding Mystical, rather than Yawg?
1: Lotus, Walk - If he is holding another mana source then he goes Lotus, Walk, Mystica-Yawg, turn 1.b, Yawg, Lotus, Tinker. If he has no more mana then this option forces him to wait a turn. If he has Drain then he can Drain our turn 1 play and then Mystical for Yawg. Next turn he uses Drain mana + Jet to cast Yawg and then casts Lotus, Tinker, Walk. Little does our opponent know that we likely have no turn relevant turn 1 play that he can Drain usefully. Basically only Brainstorm and Ponder would be relevant and generate enough Drain mana. Note that Sapphire, Lotus, Petal, Tormod's Crypt and Forces are all nice cards for us to draw here.
2: Lotus, Tinker - This allows for an immediate Tinker, but at least there will be an artifact in the yard and no access to Walk so Welder will answer. If he waits a turn he can Mystical for Yawg and then Tinker out Vault for Petal and play Yawg and Walk. This might be worse.
3: Lotus, Academy - Next turn he Mystica's for Yawg and then casts Yawg with 6 mana available allowing him to Tinker, Walk and Mystical for Drain. Ouch. Note that if he is holding Drain he could have had Drain backup when he cast Yawg.
4: Walk, Tinker - If he draws or has mana then he can Tinker and then Walk. If he has no mana then he must Walk next turn and hope to draw mana. This may actually be the best split to give him and he may have counted on the fact that no one wants to give someone Walk and Tinker.
5: Walk, Academy - He passes the turn, Mysticals for Yawg on upkeep and drops Academy and plays Yawg, Lotus, Tinker. Next turn he Walks. This is not that bad.
6: Tinker, Academy - Next turn he Mysticals for Force on upkeep and then Tinkers for DSC.
#1 and #5 mean that our opponent likely passes the turns and then casts Yawg without counter backup (unless he is already holding Force. We are screwed anyway if this is the case)
#4 If he has no land then this is the best option. If he has another mana source then it is equivolent to #6 because he can Walk and Mystical for Force and then Tinker on turn b with Force backup.
#6 means he Tinker with Force backup next turn.
#3 means he casts Yawg with Drain backup next turn.
#2 means he Tinkers right now!
My conclusion here is that Brassman is still right. The best split is to give him Walk and Academy and hope that you draw Force, Sapphire, Petal, Lotus or Tormod's Crypt. Lotus and Academy is slightly worse because if he is holding another mana source he can Tinker now.
Finally, Tinker and Walk might work out if he is counting on drawing into more mana. Since this is a game we are likely to lose either way, perhaps this gamble is best.